Problem Statement

Solve the following problem for $T$ test cases.

You are given a sequence $A$ of length $N$ consisting of $0,1$. You may perform the following operation on this sequence $N-1$ times.

• Remove $2$ adjacent elements and replace them with their average.

Determine whether it is possible to make $A=(0.5)$.

Input

$T$
$\text{case}_1$
$\text{case}_2$
$\vdots$
$\text{case}_T$

Each case is given in the following format.

$N$
$A_1$ $A_2$ $\ldots$ $A_N$

• $1 \le T \le 2 \times 10^5$
• $1 \le N \le 2 \times 10^5$
• $A_i \in \{0,1\}$
• The sum of $N$ over all cases does not exceed $2\times 10^5$.
• All input values are integers.

Output

Print $T$ lines. On the $i$-th line, print the answer for $\text{case}_i$. For each case, print Yes if it is possible, and No if it is impossible.

Sample

3
6
1 0 1 0 0 1
5
0 1 0 1 0
9
1 1 0 1 0 0 0 1 0

Yes
No
Yes